One of the fundamental issues in computer science computation is the representation of numbers, specifically integers, real numbers and complex numbers. Although there are bit lengths that can easily accommodate the result of most integer and real number computations, problems arise when a required bit length is fixed or predetermined and the computation includes the manipulation and storage of complex numbers. The primary reason for this is that complex numbers include two (2) components, or a “real” and an “imaginary” component.
Each component is typically represented as a floating point number, which comprises three fields: a sign, a significand, or “mantissa,” and an exponent. The sign field represents whether the corresponding number is positive or negative. According to IEEE standard 754 for floating point numbers, the mantissa field is defined as an explicit or implicit leading bit to the left of the number's implied binary point and a fraction field to its right. The exponent field represents the power to which a base number must be raised to generate the represented number.
If sixteen (16) bits are reserved for each of the real and imaginary components of a complex number, typically, one (1) bit is employed for the sign, either two (2) or four (4) bits are employed for the exponent, and the remaining thirteen (13) or eleven (11) bits, respectively, are employed for the mantissa.
A method is needed for the storage of complex numbers in a computing or communication system. One such communication system that deals with complex numbers includes digital subscriber line type systems. The ADSL and VDSL are exemplary types of digital subscriber communication systems. The VDSL standard as provided by the ANSI T1E1.4 Technical Subcommittee, provides guidelines for the transmitter and receiver within the VDSL modem. Very high bit rate DSL (VDSL) is currently capable of providing speeds of 52 Mbps downstream and 16 Mbps upstream. ADSL is capable of 10 Mbps downstream and 800 Kbps upstream. Other standards beyond ADSL and VDSL are being considered by standards bodies. For example, VDSL2 is one such standard. To implement these current and upcoming standards, a discrete multitone (DMT) transceiver is required that can operate at higher bit rates efficiently. A method for dealing with complex numbers that allows digital subscriber line technologies to be efficient enhances the value of such technologies by reducing equipment size and maximizing communication throughput. These and other advantages of the invention, as well as additional inventive features, will be apparent from the description of the invention provided herein.